A well-known limitation of the original halo model is that mass and momentum are not conserved on large scales [1]}.
In the \(k\rightarrow 0\)  limit, conservation of these quantities requires \(\lim _{k \rightarrow 0} P_{mm} \propto k^{4}\)  [2]}.
The violation of this requirement for the halo model arises from the \(k^{0}\)  contribution of the one-halo term, which is due to the Poisson contribution from a finite number of halos [3]}.
The HZPT model address this by multiplying the BB Padé expansion term by a compensation kernel \(F(k)\) , which suppresses the low-\(k\)  \(k^{0}\)  contribution (though at leading order this term goes like \(k^{2}\) ).
It is possible to explore more complicated forms of the compensation kernel (MS14), or to compensate the functional form of the halo profile iteslf [4]}, but here we keep with the previous iterations of HZPT and use the simple Lorentzian kernel with a single parameter \(R\) :
\(F(k) = \left( 1 - \frac{1}{1 + k^{2} R^{2}} \right).\) 
